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301
Surface Reconstruction by Voronoi Filtering
 Discrete and Computational Geometry
, 1998
"... We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled ..."
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Cited by 418 (15 self)
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We give a simple combinatorial algorithm that computes a piecewiselinear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on "local feature size", the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a surface from scattered sample points arises in many applications such as computer graphics, medical imaging, and cartography. In this paper we consider the specific reconstruction problem in which the input is a set of sample points S drawn from a smooth twodimensional manifold F embedded in three dimensions, and the desired output is a triangular mesh with vertex set equal to S that faithfully represen...
Point Set Surfaces
, 2001
"... We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We pre ..."
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Cited by 298 (42 self)
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We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.
Illustrating Smooth Surfaces
 PROCEEDINGS OF SIGGRAPH 2000
, 2000
"... We present a new set of algorithms for lineart rendering of smooth surfaces. We introduce an efficient, deterministic algorithm for finding silhouettes based on geometric duality, and an algorithm for segmenting the silhouette curves into smooth parts with constant visibility. These methods can be ..."
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Cited by 288 (10 self)
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We present a new set of algorithms for lineart rendering of smooth surfaces. We introduce an efficient, deterministic algorithm for finding silhouettes based on geometric duality, and an algorithm for segmenting the silhouette curves into smooth parts with constant visibility. These methods can be used to find all silhouettes in real time in software. We present an automatic method for generating hatch marks in order to convey surface shape. We demonstrate these algorithms with a drawing style inspired by A Topological Picturebook by G. Francis.
Interpolating Subdivision for Meshes with Arbitrary Topology
"... Subdivision is a powerful paradigm for the generation of surfaces of arbitrary topology. Given an initial triangular mesh the goal is to produce a smooth and visually pleasing surface whose shape is controlled by the initial mesh. Of particular interest are interpolating schemes since they match the ..."
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Cited by 239 (24 self)
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Subdivision is a powerful paradigm for the generation of surfaces of arbitrary topology. Given an initial triangular mesh the goal is to produce a smooth and visually pleasing surface whose shape is controlled by the initial mesh. Of particular interest are interpolating schemes since they match the original data exactly, and play an important role in fast multiresolution and wavelet techniques. Dyn, Gregory, and Levin introduced the Butterfly scheme, which yields C 1 surfaces in the topologically regular setting. Unfortunately it exhibits undesirable artifacts in the case of an irregular topology. We examine these failures and derive an improved scheme, which retains the simplicity of the Butterfly scheme, is interpolating, and results in smoother surfaces.
Subdivision surfaces in character animation
 In Proceedings of the 25th annual conference on Computer graphics and interactive techniques, SIGGRAPH ’98
, 1998
"... The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the seve ..."
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Cited by 235 (1 self)
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The creation of believable and endearing characters in computer graphics presents a number of technical challenges, including the modeling, animation and rendering of complex shapes such as heads, hands, and clothing. Traditionally, these shapes have been modeled with NURBS surfaces despite the severe topological restrictions that NURBS impose. In order to move beyond these restrictions, we have recently introduced subdivision surfaces into our production environment. Subdivision surfaces are not new, but their use in highend CG production has been limited. Here we describe a series of developments that were required in order for subdivision surfaces to meet the demands of highend production. First, we devised a practical technique for constructing provably smooth variableradius fillets and blends. Second, we developed methods for using subdivision surfaces in clothing simulation including a new algorithm for efficient collision detection. Third, we developed a method for constructing smooth scalar fields on subdivision surfaces, thereby enabling the use of a wider class of programmable shaders. These developments, which were used extensively in our recently completed short film Geri’s game, have become a highly valued feature of our production environment.
Survey of Polygonal Surface Simplification Algorithms
, 1997
"... This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons ..."
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Cited by 228 (3 self)
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This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons
Interactive Multiresolution Mesh Editing
"... We describe a multiresolution representation for meshes based on subdivision. Subdivision is a natural extension of the existing patchbased surface representations. At the same time subdivision algorithms can be viewed as operating directly on polygonal meshes, which makes them a useful tool for me ..."
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Cited by 215 (20 self)
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We describe a multiresolution representation for meshes based on subdivision. Subdivision is a natural extension of the existing patchbased surface representations. At the same time subdivision algorithms can be viewed as operating directly on polygonal meshes, which makes them a useful tool for mesh manipulation. Combination of subdivision and smoothing algorithms of Taubin [26] allows us to construct a set of algorithms for interactive multiresolution editing of complex meshes of arbitrary topology. Simplicity of the essential algorithms for re nement and coarsi cation allows to make them local and adaptive, considerably improving their efficiency. We have built a scalable interactive multiresolution editing system based on such algorithms.
Automatic reconstruction of Bspline surfaces of arbitrary topological type
 SIGGRAPH'96
, 1996
"... Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners in ..."
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Cited by 174 (0 self)
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Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product Bspline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single Bspline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of Bspline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the Bspline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy userspecified error tolerances, and demonstrate our method on both synthetic and real data.